$2\mathrm{.}3$ A flanged beam has the effective section shown in Fig. Q$-2\mathrm{.}3.$ Characteristic strengths are: $f_{ck}=30$MPa,$f_{yk}=500$MPa.

$($a$)$ Determine the maximum positive moment of resistance of the singly reinforced section based on allowable maximum value of $\frac{x}{d}$ of $0\mathrm{.}45,$ and the corresponding area of tension reinforcement. Use $H25$ bars and assume an effective depth of $600mm.$

$($b$)$ Determine the overall depth of the beam assuming a cover of $50mm$ to reinforcing bars and a clear spacing of $25mm$ between rows of bars.

$($c$)$ Using the results obtained in $($b$)$ above, determine the maximum negative moment that can be resisted by the singly reinforced section and the area of tension reinforcement required in the flange. Use $H25$ bars and assume a clear cover of $50mm.$